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This study aims to analyze the effect of using Collaborative Problem-Based Learning (CPBL) on students' problem-solving skills. This study used a 2x2 factorial design, in which the selection of experimental and control groups was determined with convenience sampling. The data analysis technique of this research is divided into two types, namely the prerequisite analysis test and hypothesis testing. The findings of this study concluded that students who studied with CPBL had significantly higher problem-solving skills than students who studied with Direct Instruction (DI). In addition, high problem-solving skills were generally owned by students with high initial skills. Meanwhile, the complete the results of the hypothesis test this study also showed a significant interaction between the learning model and initial skills on students' problem-solving skills in internal combustion motor competences. This shows that the selection of the right learning model is needed according to the initial skills of students so that problem-solving skills can be adequately developed. Thus, it is hoped that vocational school students can become graduates who can compete in the world of work.

Learning design is one of the factors that support the learning process in order to achieve learning objectives in all subjects including mathematics. Many approaches can be employed by a teacher in making learning design, one of which is rigorous mathematical thinking (RMT) approach. The RMT approach puts forward students actively in constructing their knowledge through the use of psychological tools and mediation. This article reports a set of learning activities designed through a developmental study using the RMT approach in the topic of application of derivatives. Participants of this research were twenty-six of 11th grade students from a private secondary school. Data were collected through written test and classroom observation. The research instruments were student worksheet and observation sheet. In the learning process, students use psychological tools to connect their previous knowledge to the material being studied. This makes students able to construct their own knowledge more thoroughly. On the other hand, with the mediation carried out by the teacher, students can focus more and understand each material well and bridge the conceptual errors. Based on the results of the study and some literature, Design of learning activities using Rigorous Mathematical Thinking (RMT) on application of derivative can be an alternative as effective learning.

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